Left adjoint of pullback $Cat^1$-groups

Left adjoint of pullback $Cat^1$-groups

In [1] we define the pullback $Cat^1$-groups and showed that the category of pullback $Cat^1$-groups is equivalent to the category of pullback crossed modules. In this paper we proved that the pullback $Cat^1$-group has a left adjoint which is the induced $Cat^1$-group. We also give the left adjoint construction.

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